Objectives

  1. Assess concerns over data availability.
  2. Investigate multicollinearity between our three continuous covariates: flow, spill, and temperature.
  3. Look at passage timing, to determine when covariate data will be most useful.
  4. Decide how covariate data will be matched to state occupancy (e.g., a window approach)

Matching covariate data to state occupancy

Example of movements for one fish:

##                            state           date_time      pathway
## 2223        mainstem, BON to MCN 2014-08-16 11:53:22  BON (adult)
## 2224 mainstem, MCN to ICH or PRA 2014-09-20 05:23:09  MCN (adult)
## 2225        mainstem, PRA to RIS 2014-09-24 05:30:10  PRA (adult)
## 2226        mainstem, RIS to RRE 2014-09-29 07:00:14     implicit
## 2227        mainstem, RRE to WEL 2014-09-29 07:00:14  RRE (adult)
## 2228   mainstem, upstream of WEL 2014-10-03 08:05:33  WEL (adult)
## 2229       Methow River Upstream 2014-10-20 05:52:58 MET_upstream
## 2230   mainstem, upstream of WEL 2014-11-13 10:17:14     implicit
## 2231        mainstem, RRE to WEL 2014-11-13 10:17:14     implicit
## 2232        mainstem, RIS to RRE 2014-11-13 10:17:14     implicit
## 2233        mainstem, PRA to RIS 2014-11-13 10:17:14     implicit
## 2234 mainstem, MCN to ICH or PRA 2014-11-13 10:17:14     implicit
## 2235        mainstem, ICH to LGR 2014-11-13 10:17:14  ICH (adult)
## 2236   mainstem, upstream of LGR 2014-11-26 13:54:45  LGR (adult)
## 2237                Salmon River 2015-03-28 01:19:45    SAL_sites

Covariate Data

Summary

  • The following dams lack winter (November - Feburary) temperature data: Bonneville, Rock Island (until 2012), Rocky Reach (until 2012), Wells Dam (until 2013)
  • Spill data can be a bit patchy - are missing spill values zeros?
  • Spill and flow are strongly correlated; VIF vary, but are between 2 and 8. R^2 values range 0.55 - 0.9
  • In some years, spill appears to follow the relationship spill = flow - X, but the value of X changes from year to year. This appears to be especially true for the four Snake River Dams

Bonneville Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                3607                3425

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -92.339 -22.198  -6.513  20.017  87.547 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -58.580290   1.058786  -55.33   <2e-16 ***
## flow          0.581807   0.005398  107.79   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 36.62 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.623,  Adjusted R-squared:  0.623 
## F-statistic: 1.162e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.737  -3.851   1.940   4.272   7.149 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 19.799147   0.231904   85.38   <2e-16 ***
## flow        -0.021936   0.001043  -21.02   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.173 on 3423 degrees of freedom
##   (3880 observations deleted due to missingness)
## Multiple R-squared:  0.1144, Adjusted R-squared:  0.1141 
## F-statistic:   442 on 1 and 3423 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -88.259 -37.269   7.213  24.494 200.329 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  60.7130     2.6640  22.790  < 2e-16 ***
## temp          1.2691     0.1639   7.741 1.29e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 52.72 on 3423 degrees of freedom
##   (3880 observations deleted due to missingness)
## Multiple R-squared:  0.01721,    Adjusted R-squared:  0.01692 
## F-statistic: 59.92 on 1 and 3423 DF,  p-value: 1.289e-14

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.129121 1.129121 
## 
## [[2]]
##   flow  spill 
## 2.1435 2.1435 
## 
## [[3]]
##    spill     temp 
## 1.017506 1.017506

John Day Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 448                6584

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -90.623 -14.601  -0.062  16.228  92.384 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -56.161515   0.671859  -83.59   <2e-16 ***
## flow          0.534644   0.003576  149.50   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 24.62 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.7607, Adjusted R-squared:  0.7607 
## F-statistic: 2.235e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.5939  -6.1873   0.3332   5.9630  10.5648 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 13.2905210  0.1790238  74.239   <2e-16 ***
## flow        -0.0043790  0.0009367  -4.675    3e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.371 on 6582 degrees of freedom
##   (721 observations deleted due to missingness)
## Multiple R-squared:  0.00331,    Adjusted R-squared:  0.003158 
## F-statistic: 21.86 on 1 and 6582 DF,  p-value: 2.998e-06
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -55.08 -28.91 -19.88  17.34 247.57 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.29933    1.35100   9.104   <2e-16 ***
## temp         1.92895    0.09603  20.087   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 49.72 on 6582 degrees of freedom
##   (721 observations deleted due to missingness)
## Multiple R-squared:  0.05776,    Adjusted R-squared:  0.05762 
## F-statistic: 403.5 on 1 and 6582 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.003321 1.003321 
## 
## [[2]]
##     flow    spill 
## 4.219045 4.219045 
## 
## [[3]]
##    spill     temp 
## 1.061299 1.061299

The Dalles Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 280                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 434                6591

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -101.903  -16.900    0.344   20.779  126.049 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -60.435506   0.778870  -77.59   <2e-16 ***
## flow          0.582702   0.004264  136.66   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27.74 on 7023 degrees of freedom
##   (280 observations deleted due to missingness)
## Multiple R-squared:  0.7267, Adjusted R-squared:  0.7267 
## F-statistic: 1.868e+04 on 1 and 7023 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.4977  -6.1205   0.3951   5.8010  10.4654 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 13.6825394  0.1810168  75.587  < 2e-16 ***
## flow        -0.0066120  0.0009764  -6.772 1.38e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.286 on 6589 degrees of freedom
##   (714 observations deleted due to missingness)
## Multiple R-squared:  0.006911,   Adjusted R-squared:  0.00676 
## F-statistic: 45.85 on 1 and 6589 DF,  p-value: 1.384e-11
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -62.61 -28.65 -17.73  21.11 272.82 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    7.596      1.421   5.347 9.26e-08 ***
## temp           2.441      0.101  24.168  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 51.71 on 6589 degrees of freedom
##   (714 observations deleted due to missingness)
## Multiple R-squared:  0.08143,    Adjusted R-squared:  0.08129 
## F-statistic: 584.1 on 1 and 6589 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.006959 1.006959 
## 
## [[2]]
##     flow    spill 
## 3.718405 3.718405 
## 
## [[3]]
##    spill     temp 
## 1.088647 1.088647

McNary Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                  13                7019

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -95.607 -19.844  -1.294  20.349  91.304 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -84.513785   0.849167  -99.53   <2e-16 ***
## flow          0.792072   0.004517  175.35   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 30.62 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.8139, Adjusted R-squared:  0.8139 
## F-statistic: 3.075e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.1274  -6.0829  -0.1466   5.9885  17.3149 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 11.9762940  0.1735677  69.001   <2e-16 ***
## flow        -0.0004554  0.0009228  -0.494    0.622    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.252 on 7017 degrees of freedom
##   (286 observations deleted due to missingness)
## Multiple R-squared:  3.471e-05,  Adjusted R-squared:  -0.0001078 
## F-statistic: 0.2436 on 1 and 7017 DF,  p-value: 0.6217
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -104.44  -42.03  -24.10   26.84  317.75 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  12.6647     1.7519   7.229 5.37e-13 ***
## temp          3.1375     0.1303  24.072  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 68.26 on 7017 degrees of freedom
##   (286 observations deleted due to missingness)
## Multiple R-squared:  0.07628,    Adjusted R-squared:  0.07615 
## F-statistic: 579.5 on 1 and 7017 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.000035 1.000035 
## 
## [[2]]
##     flow    spill 
## 5.373753 5.373753 
## 
## [[3]]
##    spill     temp 
## 1.082582 1.082582

Priest Rapids Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 965                6067

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -55.491 -14.096  -0.015  11.494  87.417 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -51.993141   0.629370  -82.61   <2e-16 ***
## flow          0.620771   0.004882  127.15   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 20.86 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.6969, Adjusted R-squared:  0.6969 
## F-statistic: 1.617e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.0637  -5.5323   0.2589   5.5389   9.4832 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.189562   0.185454  65.728  < 2e-16 ***
## flow        -0.006472   0.001400  -4.623 3.85e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.747 on 6065 degrees of freedom
##   (1238 observations deleted due to missingness)
## Multiple R-squared:  0.003512,   Adjusted R-squared:  0.003348 
## F-statistic: 21.38 on 1 and 6065 DF,  p-value: 3.852e-06
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -32.366 -20.686 -15.321   1.104 218.354 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.17874    1.10912   10.98   <2e-16 ***
## temp         1.01487    0.08683   11.69   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38.93 on 6065 degrees of freedom
##   (1238 observations deleted due to missingness)
## Multiple R-squared:  0.02203,    Adjusted R-squared:  0.02187 
## F-statistic: 136.6 on 1 and 6065 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.003525 1.003525 
## 
## [[2]]
##     flow    spill 
## 3.416603 3.416603 
## 
## [[3]]
##    spill     temp 
## 1.022524 1.022524

Rock Island Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                1241                5791

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.512  -8.407  -0.435   7.186 122.675 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -29.602166   0.438001  -67.58   <2e-16 ***
## flow          0.365947   0.003557  102.88   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.93 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.6009, Adjusted R-squared:  0.6008 
## F-statistic: 1.058e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.338  -5.246   1.327   5.159  10.651 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 14.064049   0.194409   72.34   <2e-16 ***
## flow        -0.017153   0.001515  -11.33   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.588 on 5789 degrees of freedom
##   (1514 observations deleted due to missingness)
## Multiple R-squared:  0.02168,    Adjusted R-squared:  0.02151 
## F-statistic: 128.3 on 1 and 5789 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -18.502 -14.556 -10.353   7.457 193.300 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.11902    0.72238  12.624   <2e-16 ***
## temp         0.45548    0.05437   8.377   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 23.37 on 5789 degrees of freedom
##   (1514 observations deleted due to missingness)
## Multiple R-squared:  0.01198,    Adjusted R-squared:  0.01181 
## F-statistic: 70.18 on 1 and 5789 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.022158 1.022158 
## 
## [[2]]
##     flow    spill 
## 2.594388 2.594388 
## 
## [[3]]
##    spill     temp 
## 1.012123 1.012123

Rocky Reach Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                1259                5773

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -38.089  -7.864  -0.540   6.408 115.994 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -30.537689   0.400374  -76.27   <2e-16 ***
## flow          0.352975   0.003356  105.19   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.97 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.6115, Adjusted R-squared:  0.6114 
## F-statistic: 1.106e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.282  -5.296   1.545   5.149   8.098 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 14.22148    0.19036   74.71   <2e-16 ***
## flow        -0.01707    0.00153  -11.16   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.579 on 5771 degrees of freedom
##   (1532 observations deleted due to missingness)
## Multiple R-squared:  0.02112,    Adjusted R-squared:  0.02095 
## F-statistic: 124.5 on 1 and 5771 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.704 -10.101  -9.334   0.143 194.634 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.00495    0.71098  12.665   <2e-16 ***
## temp         0.08313    0.05268   1.578    0.115    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.57 on 5771 degrees of freedom
##   (1532 observations deleted due to missingness)
## Multiple R-squared:  0.0004312,  Adjusted R-squared:  0.000258 
## F-statistic:  2.49 on 1 and 5771 DF,  p-value: 0.1146

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.021572 1.021572 
## 
## [[2]]
##     flow    spill 
## 2.732757 2.732757 
## 
## [[3]]
##    spill     temp 
## 1.000431 1.000431

Wells Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   8                1904                5120

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -27.809  -7.107  -0.581   5.817 102.561 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -29.292950   0.362110  -80.89   <2e-16 ***
## flow          0.344634   0.003029  113.79   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.63 on 7022 degrees of freedom
##   (281 observations deleted due to missingness)
## Multiple R-squared:  0.6484, Adjusted R-squared:  0.6483 
## F-statistic: 1.295e+04 on 1 and 7022 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.477  -5.130   1.119   5.220   8.722 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 13.489958   0.199053  67.771   <2e-16 ***
## flow        -0.014769   0.001569  -9.414   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.52 on 5126 degrees of freedom
##   (2177 observations deleted due to missingness)
## Multiple R-squared:  0.017,  Adjusted R-squared:  0.0168 
## F-statistic: 88.63 on 1 and 5126 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -12.127 -11.292  -5.974  -1.496 173.559 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 10.69962    0.72078  14.844   <2e-16 ***
## temp         0.07081    0.05536   1.279    0.201    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.06 on 5118 degrees of freedom
##   (2185 observations deleted due to missingness)
## Multiple R-squared:  0.0003196,  Adjusted R-squared:  0.0001243 
## F-statistic: 1.636 on 1 and 5118 DF,  p-value: 0.2009

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.018223 1.018223 
## 
## [[2]]
##     flow    spill 
## 3.130486 3.130486 
## 
## [[3]]
##   spill    temp 
## 1.00032 1.00032

Ice Harbor Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                  15                7017

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -51.649  -6.195  -0.357   8.586  38.600 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -13.724519   0.227780  -60.25   <2e-16 ***
## flow          0.689502   0.003906  176.52   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 11.87 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.8159, Adjusted R-squared:  0.8159 
## F-statistic: 3.116e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.6940  -6.2951   0.2389   5.8858  10.6578 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.348746   0.123392 100.078  < 2e-16 ***
## flow        -0.007396   0.002115  -3.497 0.000473 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.42 on 7015 degrees of freedom
##   (288 observations deleted due to missingness)
## Multiple R-squared:  0.00174,    Adjusted R-squared:  0.001598 
## F-statistic: 12.23 on 1 and 7015 DF,  p-value: 0.0004731
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.431 -15.915 -12.082   6.604 140.958 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  9.60196    0.69138   13.89   <2e-16 ***
## temp         0.68310    0.05076   13.46   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27.32 on 7015 degrees of freedom
##   (288 observations deleted due to missingness)
## Multiple R-squared:  0.02517,    Adjusted R-squared:  0.02503 
## F-statistic: 181.1 on 1 and 7015 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.001743 1.001743 
## 
## [[2]]
##     flow    spill 
## 5.425536 5.425536 
## 
## [[3]]
##    spill     temp 
## 1.025818 1.025818

Lower Monumental Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 280                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 461                6564

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.056  -4.884  -1.055   5.794  61.922 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -7.348479   0.201406  -36.49   <2e-16 ***
## flow         0.407361   0.003545  114.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.39 on 7023 degrees of freedom
##   (280 observations deleted due to missingness)
## Multiple R-squared:  0.6528, Adjusted R-squared:  0.6528 
## F-statistic: 1.321e+04 on 1 and 7023 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.493  -6.154   0.397   5.777   9.999 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.54669    0.12457 100.717  < 2e-16 ***
## flow        -0.01139    0.00214  -5.325 1.04e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.185 on 6562 degrees of freedom
##   (741 observations deleted due to missingness)
## Multiple R-squared:  0.004303,   Adjusted R-squared:  0.004151 
## F-statistic: 28.36 on 1 and 6562 DF,  p-value: 1.043e-07
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.928 -10.226  -7.655   3.084 126.833 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.07526    0.47818   12.71   <2e-16 ***
## temp         0.46397    0.03535   13.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.75 on 6562 degrees of freedom
##   (741 observations deleted due to missingness)
## Multiple R-squared:  0.02558,    Adjusted R-squared:  0.02543 
## F-statistic: 172.2 on 1 and 6562 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.004321 1.004321 
## 
## [[2]]
##     flow    spill 
## 2.870193 2.870193 
## 
## [[3]]
##    spill     temp 
## 1.026247 1.026247

Little Goose Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 280                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 454                6571

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.082  -3.093   0.254   3.232 110.353 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -9.176430   0.180752  -50.77   <2e-16 ***
## flow         0.432874   0.003262  132.72   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.341 on 7023 degrees of freedom
##   (280 observations deleted due to missingness)
## Multiple R-squared:  0.7149, Adjusted R-squared:  0.7149 
## F-statistic: 1.761e+04 on 1 and 7023 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.0070  -6.0127   0.0896   5.9639  10.1816 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.041892   0.122645  98.185   <2e-16 ***
## flow        -0.005539   0.002158  -2.566   0.0103 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.102 on 6569 degrees of freedom
##   (734 observations deleted due to missingness)
## Multiple R-squared:  0.001002,   Adjusted R-squared:  0.0008496 
## F-statistic: 6.586 on 1 and 6569 DF,  p-value: 0.0103
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.849  -9.238  -7.103   2.647 172.191 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.75320    0.47600   12.09   <2e-16 ***
## temp         0.39236    0.03584   10.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.74 on 6569 degrees of freedom
##   (734 observations deleted due to missingness)
## Multiple R-squared:  0.01791,    Adjusted R-squared:  0.01776 
## F-statistic: 119.8 on 1 and 6569 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.001003 1.001003 
## 
## [[2]]
##     flow    spill 
## 3.504784 3.504784 
## 
## [[3]]
##    spill     temp 
## 1.018239 1.018239

Lower Granite Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 273                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                  14                7018

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.194  -4.509  -0.893   4.765  51.799 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -7.984336   0.182926  -43.65   <2e-16 ***
## flow         0.421640   0.003195  131.97   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.474 on 7030 degrees of freedom
##   (273 observations deleted due to missingness)
## Multiple R-squared:  0.7124, Adjusted R-squared:  0.7124 
## F-statistic: 1.742e+04 on 1 and 7030 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.9040 -5.8980 -0.4319  6.3122 10.3850 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 11.014712   0.114800  95.947   <2e-16 ***
## flow         0.001431   0.002007   0.713    0.476    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.933 on 7016 degrees of freedom
##   (287 observations deleted due to missingness)
## Multiple R-squared:  7.241e-05,  Adjusted R-squared:  -7.011e-05 
## F-statistic: 0.5081 on 1 and 7016 DF,  p-value: 0.476
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -17.138  -8.931  -6.075   2.895 116.193 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.65041    0.43463   8.399   <2e-16 ***
## temp         0.66313    0.03458  19.175   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.19 on 7016 degrees of freedom
##   (287 observations deleted due to missingness)
## Multiple R-squared:  0.04979,    Adjusted R-squared:  0.04966 
## F-statistic: 367.7 on 1 and 7016 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.000072 1.000072 
## 
## [[2]]
##     flow    spill 
## 3.458132 3.458132 
## 
## [[3]]
##    spill     temp 
## 1.052403 1.052403

State timing

Dam ascents

Tributary entries

Dam fallback (timing estimated)